Personally, I don't want to hear crystal clear full bandwidth dynamic audio from the space shuttle or the ISS. I think the graininess and distortion add to the atmosphere. The reports from space wouldn't be the same if they were crystal clear!

I think what's being overlooked here is that the channel is for voice communications in noisy backgrounds. Well before World War II, research had shown that, under extreme noise conditions (think airplane cockpits), voices are more intelligible if the audio is high-pass filtered, hard-clipped, and then low-pass filtered. It sure isn't "hi-fi" but it vastly boosts voice intelligibility. I'll assume they were smart enough to do this on purpose. Just because it's "old school" doesn't mean it's bad ... neither is digital always better!

Hey gang, I wanted to help shed a little light on this. We do indeed have decent audio being downlinked from the International Space Station. See link. http://www.youtube.com/watch?v=ywFfI0-nu00
We have been doing this live since 2006. The other types of audio that you may hear is through our S-band system that has to have multiple redundancy and back up systems for critical communications. Qualifying hardware for space flight is challenging. As electronic components become smaller and smaller, they tend to be more susceptible to radiation. Downlink from the ISS is 150 Mbps.

Nice to see someone putting this in perspective!
Given the distance it's amazing we had any audio at all!
What might be even more amazing is how bad the audio is in current digital tv antenna systems, where an all-or-nothing approach is used. If the video signal is too weak, the frame freezes and no attempt is even made (by the system) to send the lower-bandwidth audio.

You must remember how NASA works. They don't do anything that is faster, better, or more quality. They do things for the cheapest amount possible when the manual is written. What I mean is that if someone finds a better way to put a panel on the shuttle craft, the better way will never meet the real world as it would cost way too much to change all of the necessary and unnecessary documents NASA has.
NASA does everything through a manual. Nothing, and I mean absolutely nothing is done without planning for it ahead of time.

It's all in the microphone.
They have a broadcast quality mic aboard the Alpha/ISS, which they use occasionally. So we know at least some if not all of the audio channels are high quality.
So why does it sound "bad" the rest of the time?
Because the primary function is to GET THE MESSAGE ACROSS.
Flat broadcast-quality mics are not the best choice for that. Communications quality mics, with a tailored response (rolled-off bass, somewhat peaked upper midrange) are much better at getting the message across, even in adverse conditions like high noise and/or distortion.
Who is the intended recipient? Not you and me! Except for occasional broadcasts to the press or general public, it is other astronauts and NASA workers. They need to know WHAT was said, not how pleasant it sounds. They need to GET THE JOB DONE.
As for "'squelchy'-sounding audio", I think that's because NASA still uses squelch and PTT. They don't seem to like leaving mics live all the time. On board Alpha, their mics are PTT (push to talk) and we hear them only after they push the switch, and it may cut off the first syllable or two because some of them aren't good at it.
On spacewalks there is no PTT, they use only squelch (VOX). The environment in a spacesuit is very noisy with air conditioning running all the time, and the threshold between squelched and not squelched is a fine line; consequently a lot of noise gets through and it sounds choppy. They may also be using some sort of throat mics.
Again, it's all for the same reason: get the message across. Intelligibility wins over fidelity.
The electronics between Alpha and earth is not impaired by radiation or distance or low air pressure or age or something like that. The bandwidth needed to pass flat audio is trivial compared to passing video or high bandwidth data; and we know the audio is good quality when they use the good mic. The rest of the time, they use mics that enhance intelligibility, because that's what matters.

Hi, there's another possible cause for the noisy audio. The electronics is exposed to an ionizing radiation field much stronger than in surface earth. Even in an aircraft it is much stronger. A reverse biased junction is a good gamma and RX detector.
It must be that.

The distances, bandwidth, and just being in space, do not explain it. We satellite TV viewers receive hundreds of channels of HD TV with Dolby Digital audio from much higher orbits. Even the old analog satellite TV from the 1980's had decent mono or stereo audio. There certainly is no technical reason for poor audio from the space station.
My guess is that it may have been the best they could manage with the available power envelope for the Apollo program. When the Space Shuttle program was in the design phase they had to go with what was proven, something not far removed from the Apollo comm. Over the next 3 decades, nobody at NASA wanted to dip into their budget for the painstaking process of a comm redesign. The old comm was known to work, so a redesign was simply a low priority project that never got funded.
I propose that the poor audio quality is due simply to lack of funding.

The shuttle uses a modified ABATE algorithm as part of its telemetry stream on the S-Band. The Ku-band uses this same stream as the S-band, since the multiplexers/demux can be the same. See http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1094022 I was responsible for troubleshooting audio problems (and other telecommunications issues) on the orbiters for 7 years, and I had to help figure out when we had a problem with audio. So, the hardware, specs, TDRSS satellites, etc, was designed for that standard. Yes, even MP3 is much superior, but that was the 60s/70s when designed, and it worked. Yes, it's poor audio. It is prohibitively expensive to change, especially for NASA and all its bureaucracy. Read, for example why the railroad tracks are the width they are, it goes back to Roman times! I'm not condoning the bad audio, just trying to explain how we got where we are.